Physics, asked by shaikasifahamed4144, 1 year ago

Diffraction of x rays by crystals show that

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Answered by charlie0011
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X-ray Diffraction

One of the best methods of determining a crystal's structure is by X-ray diffraction. In macromolecular x-ray diffraction experiments, an intense beam of X-ray strikes the crystal of study. In general, crystal diffracts the X-ray beam differently, depending on its structure and orientation. The diffracted X-ray is collected by an area detector. The diffraction pattern consists of reflections of different intensity which can be used to determine the structure of the crystal. However, many different orientations of the crystal need to be collected before the true structure of the crystal can be determined.



The resolution of an X-ray diffraction detector is determined by the Bragg equation:



where d is the resolution of the detector, lambda is the incident x-ray wavelength, and theta is the angle of diffraction.

The setup of an X-ray detector is shown in the following:



The atoms in crystals interact with X-ray waves in such a way as to produce interference. Because crystal structures contain planes of atoms, each plane will reflect incident X-rays differently. For example, let two monochromatic X-ray beams (of a specific wavelength) strike a crystal structure at an incoming angle of theta. Ray 1 will reflect off of the top atomic plane while Ray 2 will reflect from the second atomic plane. However, because Ray 2 has to cross deeper into the atomic plane, it travels a distance 2a farther than Ray 1. If the distance 2a is equal to the integral number (n*lambda) of wavelength of two waves, then Ray 1 and 2 will be in phase, thus constructively interfere, when they both exit the crystal.



From Bragg's law, we know that n*lambda = 2d sin theta, therefore if we know the wavelength lambda of the X-rays going in to the crystal, and we can measure the angle theta of the diffracted X-rays coming out of the crystal, then we can determine the spacing between the atomic planes. This spacing is the called the d-spacing. If we now reorient the crystal to a different atomic plane, we can measure the d-spacing in other planes. By doing multiple x-ray diffractions at different crystal orientations, we can determined crystal structure and the size of the unit cell of the crystal.

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